Finite-element modeling of rate dependent mechanical properties in nanocrystalline materials

A generalized self-consistent polycrystal model is used to study the mechanical properties of polycrystalline metals as the grain size decreases from the ultra-fine size to the nanometer scale. The model takes each oriented grain and its immediate grain boundary to form a pair. Then by making use of a composite model, the nonlinear behavior of the nanocrystalline polycrystal is determined. The finite-element method is employed in conjunction with the unit cell of the composite to investigate the rate-dependent tensile behavior of the system. A dislocation density based constitutive equation is used to describe the plastic flow behavior of the grain interior. The boundary phase is assumed to have the mechanical properties of quasi-amorphous material. The constitutive equations for both grain interior and boundary phase are implemented into a finite-element program and the results of the calculations are compared with previously published experimental data. For some cases, an optimization procedure was used to tune some parameters of the model in order to decrease the distance between the calculated and experimental stress–strain curves. The agreement between results indicates the suitability of the updated model for nanocrystalline materials.